Question

Fie triunghiulABC dreptunghic in A si inaltimea AD⊥ BC . Sa se afle:
BD, Cd si Ad daca BC=26 cm si raportul dintre db si dc este 4/9

Answer 1

[tex]\it \dfrac{BD}{DC} = \dfrac{4}{9} \Rightarrow \dfrac{BD}{4} = \dfrac{DC}{9} =\dfrac{BD+DC}{4+9} = \dfrac{BC}{13} = \dfrac{26}{13} = 2\Rightarrow \\ \\ \\ \Rightarrow \begin{cases}\it BD=4\cdot2=8cm\\ \\ \it DC = 9\cdot2= 18cm\end{cases}[/tex]

$\it T.h. \Rightarrow AD^2= BD\cdot DC=8\cdot18=144\Rightarrow AD=\sqrt{144} = 12cm$